Three-dimensional occlusal and interproximal contact detection and display using virtual tooth models

ABSTRACT

Occlusal contact between upper and lower virtual three-dimensional teeth of a patient when the upper and lower arches are in an occlused condition are determined and displayed to the user on a user interface of a general purpose computing device. Various techniques for determining occlusal contacts are described. The areas where occlusal contact occurs is displayed on the user interface in a readily perceptible manner, such as by showing the occlusal contacts in green. If the proposed set-up would result in a interpenetration of teeth in opposing arches, such locations of interpenetration are illustrated in a contrasting color or shading (e.g., red). The ability to calculate distances and display occlusal contacts in a proposed set-up assists the user in planning treatment for the patient. The process can be extended to interproximal contact detection as well. The concepts also apply to dental prosthetics, such as crowns, fillings and dentures.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This is a continuation in part of U.S. patent application Ser.No. 09/835,031 filed Apr. 13, 2001, which is a continuation in part ofSer. No. 09/560,640 filed Apr. 28, 2000 and Ser. No. 09/451,609 filedNov. 30, 1999, now U.S. Pat. No. 6,250,918. This is also a continuationin part of U.S. patent application Ser. No. 09/835,039 filed Apr. 13,2001. The entire contents of each of the related applications andpatents is incorporated by reference herein.

BACKGROUND OF THE INVENTION

[0002] A. Field of the Invention

[0003] This invention relates generally to the fields of dentistry andorthodontics. More particularly, the invention relates to methods forevaluating the areas of contact, and near contact, between upper andlower teeth when the upper and lower arches are in a closed or occludedcondition. Knowledge of such areas of contact (“occlusal contacts”herein) is helpful in planning orthodontic treatment. The presentinvention provides methods of determining and displaying such occlusalcontacts using a computer and three-dimensional virtual models of teeth.

[0004] B. Description of Related Art

[0005] In orthodontics, a patient suffering from a malocclusion istypically treated by bonding brackets to the surface of the patient'steeth. The brackets have slots for receiving an archwire. Thebracket-archwire interaction governs forces applied to the teeth anddefines the desired direction of tooth movement. Typically, the bends inthe wire are made manually by the orthodontist. During the course oftreatment, the movement of the teeth is monitored. Corrections to thebracket position and/or wire shape are made manually by theorthodontist.

[0006] The key to efficiency in treatment and maximum quality in resultsis a realistic simulation of the treatment process. Today'sorthodontists have the possibility of taking plaster models of the upperand lower jaw, cutting the model into single tooth models and stickingthese tooth models into a wax bed, lining them up in the desiredposition, the so-called set-up. This approach allows for reaching aperfect occlusion without any guessing. The next step is to bond abracket at every tooth model. This would tell the orthodontist thegeometry of the wire to run through the bracket slots to receive exactlythis result. The next step involves the transfer of the bracket positionto the original malocclusion model. To make sure that the brackets willbe bonded at exactly this position at the real patient's teeth, smalltemplates for every tooth would have to be fabricated that fit over thebracket and a relevant part of the tooth and allow for reliableplacement of the bracket on the patient's teeth. To increase efficiencyof the bonding process, another option would be to place each singlebracket onto a model of the malocclusion and then fabricate one singletransfer tray per jaw that covers all brackets and relevant portions ofevery tooth. Using such a transfer tray guarantees a very quick and yetprecise bonding using indirect bonding.

[0007] However, it is obvious that such an approach requires an extremeamount of time and labor and thus is too costly, and this is the reasonwhy it is not practiced widely. The normal orthodontist does notfabricate set-ups; he places the brackets directly on the patient'steeth to the best of his knowledge, uses an off-the-shelf wire and hopesfor the best. There is no way to confirm whether the brackets are placedcorrectly; and misplacement of the bracket will change the directionand/or magnitude of the forces imparted on the teeth. While at thebeginning of treatment things generally run well as all teeth start tomove at least into the right direction, at the end of treatment a lot oftime is lost by adaptations and corrections required due to the factthat the end result has not been properly planned at any point of time.For the orthodontist this is still preferable over the lab processdescribed above, as the efforts for the lab process would still exceedthe efforts that he has to put in during treatment. And the patient hasno choice and does not know that treatment time could be significantlyreduced if proper planning was done.

[0008] U.S. Pat. No. 5,431,562 to Andreiko et al. describes acomputerized, appliance-driven approach to orthodontics. In this method,certain shape information of teeth is acquired. A uniplanar targetarchforrn is calculated from the shape information. The shape ofcustomized bracket slots, the bracket base, and the shape of anorthodontic archwire, are calculated in accordance with amathematically-derived target archform. The goal of the Andreiko et al.method is to give more predictability, standardization, and certainty toorthodontics by replacing the human element in orthodontic appliancedesign with a deterministic, mathematical computation of a targetarchform and appliance design. Hence the '562 patent teaches away froman interactive, computer-based system in which the orthodontist remainsfully involved in patient diagnosis, appliance design, and treatmentplanning and monitoring.

[0009] More recently, in the late 1990's Align Technologies beganoffering transparent, removable aligning devices as a new treatmentmodality in orthodontics. In this system, a plaster model of thedentition of the patent is obtained by the orthodontist and shipped to aremote appliance manufacturing center, where it is scanned with a laser.A computer model of the dentition in a target situation is generated atthe appliance manufacturing center and made available for viewing to theorthodontist over the Internet. The orthodontist indicates changes theywish to make to individual tooth positions. Later, another virtual modelis provided over the Internet and the orthodontist reviews the revisedmodel, and indicates any further changes. After several such iterations,the target situation is agreed upon. A series of removable aligningdevices or shells are manufactured and delivered to the orthodontist.The shells, in theory, will move the patient's teeth to the desired ortarget position. Representative patents describing the Align processinclude U.S. Pat. Nos. 6,217,325; 6,210,162; and 6,227,850, which areincorporated by reference herein.

[0010] Other patents addressed to planning treatment for a patientinclude Doyle, U.S. Pat. No. 5,879,158, Wu et al., U.S. Pat. No.5,338,198 and Snow et al., U.S. Pat. No. 6,068,482.

[0011] Orthodontics and dentistry involves the three-dimensional spatialpositioning of teeth to get the best possible fit. Critical to thesuccess is the relative position of the teeth within the arch and withthe opposing arches. The determinants of these relationships is drivenby both the location and shape/form of the teeth. Although teeth may beideally localized spatially their fit may be poor because the shape ofthe teeth is improper. Determination of the fit between teeth can bebest estimated by defining the contact points/areas between them.Therefore, if the teeth are located correctly and the contact points arenot, it may be assumed there are discrepancies in the shape of theteeth. Location of these discrepancies is vital to achieve the desiredocclusion.

[0012] Present approaches to defining or identifying these discrepanciesare at best empirical. In current orthodontic and dental practice,occlusal contacts are determined by an orthodontist or dentist by usinga color coated, thin plastic sheet known as “articulating paper”. Thepatient “bites” onto this foil, and the color is transferred onto thetooth surface, thus indicating where teeth have occlusal contact. Thistechnique is contact-based and provides no quantitative data in terms ofdegree of poor fit.

[0013] In accordance with one aspect, the present invention provides fora simulation of this determination and display of occlusal contact usingcomputer techniques and a virtual model of the patient's dentition. Thedetermination and display of the occlusal contacts during treatmentplanning, prior to initiating treatment, allows for the orthodontist tobetter optimize the set-up on the computer. For example, theorthodontist may realize that the set up should be modified by movingone or more teeth relative to the opposing arch to provide for betterocclusal contact or prevent a collision between teeth during movement ofthe teeth from initial to finish positions. Once this more optimal toothset up has been determined, an appliance to move teeth to the desiredpositions can be designed and fabricated. The present invention isapplicable to appliance systems generally and is not limited to abracket and wire approach to straightening teeth.

SUMMARY OF THE INVENTION

[0014] In a first aspect, a method is provided for determining theproximity of teeth of upper and lower jaws of a patient. The methodincludes the steps of:

[0015] a) storing data representing three-dimensional models of teethfrom the upper and lower arches of the patient in a memory associatedwith a computer; and

[0016] b) determining, with the computer and the models, distancesbetween surfaces of teeth in one of the upper and lower arches andsurfaces of teeth in the other of the upper and lower arches when theteeth of the arches are in an occluded condition representing anocclusion of the patient. Various possible methods for determining thedistances between surfaces of the teeth in the upper and lower archesare contemplated and described in detail below.

[0017] From these measurements of distances, it is possible to determinethe locations on the tooth surfaces where the teeth are in contact,where the teeth are nearly in contact, and where one or more teeth fromone arch may intrude into a tooth or teeth in the opposite arch. Forexample, a contact may be defined as occurring when the distance betweenthe surfaces is less than a predetermined threshold, such as 0.1 mm.Negative values of the distance can be associated with interpenetrationor intrusions of one tooth into the opposite tooth.

[0018] Thee distance measurements can be assigned to the variouslocations on the tooth surfaces from which the measurements are taken.It is then possible to illustrate locations where contact occurs on auser interface, such as a computer workstation having a display screen.The workstation typically includes a treatment planning program thatincludes the occlusal contact determination feature. Thus, in apresently preferred embodiment, the method further comprising the stepsof providing a user interface for displaying the three-dimensionalmodels of the teeth, displaying all or a portion of at least one of theupper and lower arches on the user interface, and indicating on themodels information associated with the calculations. For example, theareas where contact occurs can be illustrated in one color (e.g.,green), and areas in which intrusion would occur can be illustrated in asecond color (e.g., red). As an alternative, the distance calculationscan be represented in tabular or other format as numerical distanceinformation for selected portions of the teeth.

[0019] The orthodontist will typically perform the method of the presentinvention as one tool in evaluating a proposed set-up for the patient.Based on the measurements of distances between the teeth, and thepossible presence of intrusions, he or she can operate the treatmentplanning software to move the teeth relative to each other to provide amore optimal set-up. Alternatively, the orthodontist may be satisfiedwith the set-up and can deal with the intrusions by grinding away aportion of one or the other tooth involved in the intrusion so as toeliminate the intrusion.

[0020] In another aspect, a method is provided for evaluating a proposedset-up of teeth in planning treatment for an orthodontic patient. Themethod comprises the steps of:

[0021] a) obtaining a three-dimensional digital model of the teeth ofthe upper and lower arches;

[0022] b) moving the digital models of the teeth to a proposed set-upfor treating the patient;

[0023] c) calculating distances between portions of the teeth in theupper and lower arches when the teeth are positioned in an occludedcondition; and

[0024] d) displaying the virtual models of the teeth to a user in amanner such that a user can readily distinguish portions of the teeth inthe upper and lower arches in which the distance between the portions isless than a predetermined threshold.

[0025] Occlusal contact information can be determined statically, ordynamically. For example, in another embodiment of the invention theteeth are moved from an open to a closed condition and the initial areasof contact are determined and displayed. As another example, theocclusal contacts can be determined by simulating a chewing motion ofthe upper and lower arches and calculating distances between the teethduring the chewing motion to find the areas of contact between the upperand lower arches.

[0026] As another embodiment of the invention, the feature ofdetermining distances between teeth and displaying such information canbe used to determine interproximal points of contact. The feature can beextended to determining interproximal and occlusal contact for virtualprosthetic devices, such as crowns and bridges. The determination ofsuch contacts on a compute allows the clinician to evaluate theprosthetic device and optimize its, shape,, position and/or orientationso as to maximize its interproximal and occlusal relationship toadjacent and opposing teeth.

[0027] In still another aspect, the use of contact information canenable a “magnetic” function by which teeth are automatically positionedin close proximity or touching contact with an adjacent tooth or anopposing tooth. In particular, a method is provided of manipulatingvirtual teeth on a user interface of a general-purpose computer, theuser interface including a display and a pointing device. The virtualteeth includes a first virtual tooth and a second virtual tooth, thesecond virtual tooth comprising either an adjacent tooth or an opposingtooth of the first virtual tooth. The method includes the steps ofselecting the first virtual tooth with the pointing device, moving thepointing device while the first virtual tooth is selected so as to dragthe first virtual tooth in the direction of the second virtual tooth,automatically moving the first virtual tooth so as to place the firstvirtual tooth into proximity with the second virtual tooth withoutrequiring said user to drag the first virtual tooth into proximity tothe second virtual tooth. This feature simulates a magnetic attractionof the first virtual tooth to the second virtual tooth. The featuremakes design of a proposed set-up for the patient easier and less timeconsuming.

[0028] These and many other aspects and features of the variousinventions disclosed and claimed herein will be explained in more detailin the following description of a presently preferred implementation.

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Presently preferred embodiments of the invention are describedbelow in conjunction with the appended drawing figures, where likereference numerals refer to like elements in the various views, andwherein:

[0030]FIG. 1 is a view of a set of virtual three-dimensional toothmodels representing the teeth of the lower arch of a patient, as theymight be presented on the screen of a computer. The teeth have beenmoved from a maloccluded condition to a proposed set-up or finishposition using a treatment planning program. The portions of teeth thatwould have occlusal contact with the teeth on the upper arch are shownin a contrasting color or shading to assist the orthodontist inevaluating the proposed set-up.

[0031]FIG. 2 is another view of a portion of the upper and lower archesof the patient in the proposed set-up, with the view taken from thelingual side of the arches, showing the spatial relationship of theteeth of the upper and lower arches with the occlusal contacts on theteeth of the upper arch shown in a contrasting color or shading

[0032]FIG. 3 is a view of a molar of a virtual three dimensional toothwith one portion of the tooth cusp shown on one color (e.g., green) toshow areas which are occlusal contact with the opposite tooth andanother portion shown in a second color (e.g., red) showing areas inwhich the opposite tooth would interpenetrate the tooth in the proposedset-up, thereby indicating the need to revise the treatment plan.

[0033]FIG. 4 is a schematic representation of a tooth in the upper andlower arches, illustrating one method to determine the distance betweenportions of the teeth.

[0034]FIG. 5 is a schematic representation of a tooth in the upper andlower arches, illustrating an alternative method to determine thedistance between portions of the teeth.

[0035]FIG. 6 is a schematic representation of a tooth in the upper andlower arches, illustrating one of the disadvantages to the method ofFIG. 5.

[0036]FIG. 7 is a schematic representation of a tooth in the upper andlower arches, illustrating an alternative method to determine thedistance between portions of the teeth.

[0037]FIG. 8 shows a set of teeth in one arch with parallel planesintersecting the teeth to form parallel lines, illustrating onetechnique for determining the closeness of teeth; the parallel lines canbe created vertically to determine the separation between teeth in theupper and lower arches.

[0038]FIG. 9 is a cross-section through the teeth of FIG. 8 along one ofthe planes illustrated in FIG. 8.

[0039]FIG. 10 is an illustration of a scanner and computer system thatcan be used in the practice of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Overview

[0040] The determination and display of occlusal contacts between teethin the upper and lower jaws in accordance with a preferred embodiment ofthe invention makes use of three-dimensional virtual models of teeth.The virtual models of teeth are stored in a memory and available to ageneral-purpose computer. As is known in the art, virtual models ofteeth of a patient can be obtained by using a laser scanner to scan aphysical model of the dentition. Alternatively, the teeth can be scannedin vivo, or a model of the dentition can be scanned, by a hand-heldscanner such as the type described in published PCT application ofOraMetrix, Inc., PCT/US01/11969, publication no. WO 01/80761, the entirecontents of which is incorporated by reference herein.

[0041] Once the teeth have been scanned, the three-dimensional scan datacan be represented in a a computer and displayed to the user as athree-dimensional model. There are a variety of techniques known in theCAD/CAM art for representing a three-dimensional surface, and the choiceof a particular technique or format for representation of the virtualteeth is not important. The present invention will be described incontext of a representation of a surface as a set of points that definecontiguous three-dimensional triangular shaped surface segments. Otherrepresentations of a surface such as Nonuniform Rational B Splines(NORBS) can be used. A volumetric description using voxels (a techniqueknown in the art) automatically describes a surface and that is anotherpossibility.

[0042] After the dentition, or a physical model of the dentition, hasbeen scanned, it is helpful to separate the individual teeth from therest of the anatomical structures (e.g., gingival tissue) so thatindividual teeth can be represented as independent, individualthree-dimensional virtual objects. This is described in theabove-referenced PCT application of OraMetrix. Once the teeth have beenseparated into such individual objects, CAD/CAM techniques can be usedto move the teeth relative to each other to arrive at a set-up for thepatient. A particularly advanced and highly preferred treatment planningsoftware application that performs these and other tasks is described atlength in the above-referenced PCT application of OraMetrix. Thesoftware preferably provides the user with the ability to display thearches individually, or together, either alone or in an occludedcondition. The relative position of the arches in the occluded positionis preferably user-specified by the treatment planning software. Sincethe techniques used to moved teeth and/or arches relative to each otherare already described in the patent literature, the details are omittedfrom the present discussion for the sake of brevity.

[0043] As noted above, once the teeth are represented as virtual objectsand moved to a proposed set-up representing an ideal archform for thepatient, it is possible to evaluate the set-up under a variety ofcriteria, prior to initiating treatment. One possible criteria forevaluation is the occlusal contacts. The present method of determiningand displaying occlusal contact information preferably involvesmeasuring the distance from the teeth in one arch to the teeth in theother arch, with the arches in an occluded condition. More particularly,the method involves measuring or determining the distance between aplurality of locations (points or surfaces) of one tooth and the closestlocations (i.e., surfaces or points) of teeth in the opposite arch.

[0044] In a preferred implementation, for each point (vertex) of thesurface of the digital tooth model, the closest surface point of anopposing tooth is determined. The distance can be calculated using thecomputer, since the relative positions of the teeth of both arches inthree-dimensional space is known and stored in the computer. Once thedistance has been calculated, the tooth surfaces in which the distanceis less than a predetermined threshold can be illustrated or displayedto the user in a manner that allows the user to readily perceive suchlocations. For example, the tooth surfaces which are less than 0.1 mmapart are deemed to be “occlusal contacts” and are colored or given ashading. In an example in which the surface of the teeth is representeda contiguous triangle surfaces, we can assign a color (e.g., green) or aparticular type of shading to the triangles that are associated to thepoint or surface at which the distance was calculated and the minimumdistance to the opposite tooth is less than the threshold.

[0045]FIG. 1 shows a three-dimensional virtual model of the teeth of thepatient, consisting of individual and independently moveable toothobjects or teeth 10, which have been moved by a treatment planningsoftware application to a proposed set-up. The teeth include cusps 12.The distance between locations on the surface of the teeth in the lowerarch to the teeth in the upper arch has been performed when the virtualmodel of the upper and lower arches are moved to an occluded position.The distances which are less than a threshold value, such as 0.45 mm,are shown on the monitor of the workstation in a contrasting color orshading as occlusal contact regions 14.

[0046] In one possible embodiment, it is possible to use a smoothtransition of tooth color to green. Points that are further away than0.45 mm from the opposing tooth are colored purely in tooth color.Points that contact the opposing tooth are colored in pure green. Allother points receive a color that is between tooth color and green,according to the distance. Thus, we have a continuous transition fromtooth color to green. The granularity of this transition may be limiteddepending on the typical size of the triangles defining the surface, andthe abilities of the rendering engine software that is being used todisplay those triangles at the computer monitor. Some rendering enginesdo not allow definition of colors within a triangle, but rather it isonly possible to define colors for the vertex points defining a triangleand the rendering engine will then color the triangle accordingly.However, if we had a finer triangle resolution, we would have a verysmooth transition from tooth color to green.

[0047]FIG. 2 shows another view of the upper and lower arches in theocclused condition, with the occlusal contacts shown as regions 14.

[0048] One possible color scheme for representing the occlusal contactsis as follows. If the distance between the opposing tooth and the pointor portion of the tooth to be examined is smaller than 0.45 mm, the area14 is shaded green. The value of 0.45 is somewhat arbitrary, andpreferably can be user specified by modifying a variable in a suitablescreen of the treatment planning program. The smaller the value is, thesmaller the area displayed as occlusal contact would be. Since,mathematically speaking, only one point really contacts the opposingtooth, we would only have tiny dots if we would indicate only pointsthat actually have contact. The value of 0.45 mm has been found toprovide a more useable result.

[0049] If the distance is negative, this would indicateinterpenetration, that is, a portion of one tooth has collided with theopposing tooth such that it physically projects into the other tooth.This is an undesirable outcome when planning treatment, clinicallyspeaking. Thus, when an orthodontist is planning treatment andevaluating a proposed treatment plan, whether or not suchinterpenetration between teeth of opposing arches would result is ofgreat interest to the orthodontist. The present method enables suchsituations to be determined and displayed to the user. For example, wecan show such interpenetration or negative distance values, using a redcolor to indicate the affected tooth portions. In FIG. 3, the molar 10has occlusal contact portions 14 and a region 16 shown in red whichwould be penetrated by the opposite tooth in the other arch should theproposed treatment plan be implemented and an occlusion occur.Obviously, this is undesirable since in reality teeth cannot penetrateeach other. Such a se-up would therefore represent an unrealisticscenario. The red region 16 thus alerts the orthodontist to the problem.The problem can be corrected by adjustment of the plan by simulation ofmovement of the affected tooth or teeth relative to each other toeliminate the interpenetration or by grinding the affected portions ofthe tooth or teeth.

[0050] When operating the treatment planning software for a patient witha malocclusion, the software is developed such that the user is normallyprevented from moving teeth into one another when designing a toothfinish position. However, sometimes teeth have features that may need tobe ground by the orthodontist to receive good occlusion. In such a case,the treatment planning software allows the user to override theinterpenetration prohibition feature, so that the user can indeed moveteeth into one another. The red spot 16 of FIG. 3 representing aninterpenetration tells the orthodontist very clearly and exactly, whichportion has to be ground away. The orthodontist can do this at a veryearly state of treatment. This is an advantage, since we allow the teethto readily move into the desired occlusion once a disturbing feature isground, instead of waiting and finding out very late that grinding isrequired.

[0051] In a possible alternative implementation, the software virtually“subtracts” or deletes the opposing tooth from the tooth to be ground tothereby modify the three-dimensional virtual form of the tooth to beground. This subtraction or deletion can be done using known CAD/CAMtechniques. The modified tooth shape is then displayed to the user. Thisprocedure allows the orthodontist to determine exactly not only whicharea needs to be ground, but to which shape. In yet anotherimplementation, the orthodontist grinds the tooth carefully, scans it,compares the scan data to the shape of the modified virtual tooth model,and thus determines whether and where further grinding is required.

Preferred Implementation of Contact Detection

[0052] There are several ways to determine occlusal contacts. We havepreferred a simple and fast approach, which is as follows. Withreference to FIG. 4, from each vertex point 20 (corner point of atriangle making up one element of the surface), a ray or vector 18 isconstructed running along a pre-defined direction. In a preferredimplementation, this direction is parallel to the tooth axis, which isdefined for each tooth as a central axis extending the length of thetooth through the center of the cusp. Other options are discussedfurther below. Each ray 18 is sent both to the outside and the inside ofthe tooth, as shown in FIG. 4. Then, we determine where the vectorintersects the surface of opposing teeth 10′. These points ofintersection (actually, small triangle surfaces) are shown as points 22in FIG. 4. The distance from the vertex point 20 to the intersection 22is calculated. According to the color scheme, the triangles associatedto the vertex point 20 are assigned a color depending on the distanceand the mathematical sign (positive/negative). For example, the surfacesassociated with vertex point 20 with a negative value are colored red.All surfaces 20 with a positive value less than 0.45 mm are coloredgreen. The surface where the distance is greater than or equal to 0.45mm are not colored. The virtual models of the upper and lower arches aredisplayed (typically separately) with the color information on a userinterface of the workstation implemnenting the program. See, forexample, the views shown in FIGS. 1-3.

[0053] This procedure is performed for every surface element (triangle)of the tooth. The procedure is also done for each tooth in one of thetwo arches. In one possible embodiment the user is able to modify theseparation distance variable that is indicative of an ocelusal contact(e.g., 0.45 mm). Alternatively, the separation distance can beprogrammed as a fixed parameter.

[0054] We have selected the approach of FIG. 4 because it is very fast,computationally speaking. An alternative, more sophisticated approachwould be to send the rays in the direction of a normal vector to thetooth surface. This is shown in FIG. 5, where the rays 18 are directednormal to the tooth surface 10. This alternative would require moretime, since the normal vectors I8 of FIG. 5 would have to be calculatedfor each vertex point. However, since there is no normal vector to apoint, we would have to calculate the normal vector to each trianglesurface element that the vertex belongs to, and then calculate themedian vector. The preferred embodiment described in conjunction withFIG. 4 avoids these additional computational steps and thus is quickerto perform using a state of the art microprocessor. As processing speedsimprove, the alternative method of FIG. 5 may become perfectly suitableand thus may represent a better and more accurate alternative.Additionally, the process of FIG. 5 may not by default create betterresults, as is shown in FIG. 6. Here, the normal vector 18 from point 20barely misses the tooth surface 10′, whereas the method of FIG. 4 wouldhave definitely located the surface immediately above the point 20.

[0055] An ideal method for determining the closest surface of theopposite tooth is shown in FIG. 7. The method involves creating avirtual sphere 30 around each point in the tooth 10, and increasing thediameter D of the sphere in suitable increments (e.g., 0.01 mm) untilthe sphere intersects with an opposing surface. The value of D thenindicates the proximity of the point of the tooth with the oppositetooth and this value is stored for the point. The process is done forall the points comprising the tooth surface. The treatment planningsoftware then displays the model of the teeth with all surfacescorresponding to the points for which 0<D<0.45 mm displayed in green,and all surfaces corresponding to the points for which D<0 displayed inred.

[0056] The algorithms described thus far are applicable approaches forthree-dimensional virtual objects that have a surface representationcreated by vertex points and connecting surface elements (trianglesetc.). However, there are other acceptable mathematical techniques forrepresenting arbitrary three-dimensional shapes in a computer. Thetechniques include volumetric descriptions (IGES format), and NonuniformRational B Splines (WRBS). These techniques could be used. A personskilled in the art would not have difficulty to design an appropriatealgorithm for determining occlusal contacts using these or othertechniques.

[0057] One example would be the “contour line” algorithm, which will bedescribed in conjunction with FIGS. 8 and 9. At the tooth surface,contour lines 32 are calculated in predefined planes (e.g. 0.1 mm). FIG.9 is a cross-section through the teeth along one of the contour lines32. Within each plane, such as shown in FIG. 9, a check is performed tosee if contour lines of adjacent teeth intersect. This approach couldalso be used to detect occlusal contacts. In particular, a set ofparallel planes are defined that are oriented in a vertical directioninstead of a horizontal direction. The planes will intersect thesurfaces of the upper and lower teeth, thereby forming two lines on eachplane, one for the tooth in the lower arch and the other for the toothin the upper arch, analogous to the lines shown in the cross section ofFIG. 9. The software then looks for areas in which the separationdistance between the two lines is less than a threshold. If the twolines intersect, the teeth touch. If a bounded or closed volume isformed by the two lines, then an interpenetration of the teeth hasoccurred. The contour line algorithm can be used with any kind of 3Dobject description. The technique of FIG. 9 can be used to determine theinterproximal distances between teeth, as discussed further below.

[0058] Another possible embodiment uses an “octree” data structure (aknown technique) to describe the shape of teeth. This further eases thetask of contact detection, since the data is organized in spatial cellsand the amount of data needed to represent the surface is reducedsignificantly, resulting in reduced time to calculate occlusal contacts.

[0059] One possible computer and scanner arrangement for practicing theinvention is shown in FIG. 10. An orthodontic clinic 50 is equipped witha hand-held scanner 52 which is used for either in-vivo scanning of apatient or scanning a physical model 54 of the upper and lower arches.The hand-held scanner 52 supplies scan data to a scanning node orcomputer 56 which processes the scan data to derive three-dimensionalshape data from the arches. This data is supplied to a general-purposecomputer 58 having a user interface 60. The computer 58 is equipped withor accessible to a memory (not shown) storing the tooth models and aninteractive treatment planning software. The software separates theindividual teeth from the surrounding anatomical structures and allowsthe user to interactively and selectively move the teeth to a desireddental archform for both upper and lower arches. One possible embodimentof a scanner and workstation providing treatment planning software forvirtual teeth of the upper and lower arches is described in the PCTapplication of OraMetrix, Inc., referenced previously. The workstationalso includes occlusal contact and detection tools as described abovethat allow the orthodontist to view the virtual teeth 10 on theworkstation with the occlusal contacts illustrated in a contrastingcolor (such as red or green).

[0060] The workstation or computer 58 is shown coupled via the Internet62 to a remote facility having an orthodontic server 64. In one possibleembodiment, the scan data from the scanner 52 is sent to the remotefacility and the orthodontic server 64 generates an initial treatmentplan for the orthodontist to review. The occlusal contact detection anddisplay can of course occur at the orthodontic server. Similarly thevirtual model of the teeth may be sent electronically to other locationsand shared and viewed by other health care professionals that aretreating the patient.

[0061] The collision or contact detection features described aboveenable another useful feature in planning treatment for a patient. Thisadditional feature is that when one virtual tooth is moved to a newlocation, the tooth is automatically moved into close proximity ortouching contact with the adjacent or opposite tooth. This featurestreamlines the process of designing proposed set-ups for a patient, asit keeps all the teeth together and places them in contact in the arch.This technique is referred to herein as a “magnetic” function.

[0062] The collision detection/prevention functionality is possible dueto a feature of the Windows® operating system. Whenever the mouse ismoved, the operating system not only places the mouse pointer at therespective location at the screen. It also sends a message to theprogram that owns the window where the mouse pointer is currently beingmoved over. This message is sent over and over, as long as the mouse ison the move. The message includes the current location of the mousepointer. The same thing happens (obviously only once), when you clickthe mouse or release the mouse. This functionality is a fundamentalaspect of 3D software running on a Windows® operating system. In ourimplementation, the user clicks the mouse. We store the respectivelocation of the mouse pointer. The user moves the mouse. The operatingsystem continuously sends messages containing the current location ofthe mouse pointer. Our presently preferred treatment planning softwarecalculates the distance that the mouse pointer has covered and thedirection, and we then move the 3D object that is currently selectedrespectively, and immediately display the new location on the screen.This is one way how the user can move a virtual object such as a tooth.However, before simply moving the object in accordance with the mousemovements, we can perform any kind of calculations, such as distancecalculations to opposing or adjacent teeth. If the collision preventionfeature is enabled or active, we calculate the remaining distance to theopposing (or adjacent) tooth. If this distance is smaller than thedistance that the user indicated by mouse movement, we simply move theobject only according to the remaining distance. To the user, this looksas if the object is hitting the opposing or adjacent object and cannotmove any further.

[0063] When the magnetic functionality is activated, and the user hasselected a tooth and starts moving it by dragging with the mouse, wecalculate the remaining distance to the opposing tooth and immediatelymove the tooth over the complete distance, no matter how far the mousehas really been moved. So the selected tooth will immediately get incontact with its opponent. This calculation is performed on all mousemovements, whether they indicate translations or rotations. The distancebetween the selected tooth and its opponent is kept to zero, so that thetooth appears to be “magnetically” attached to its opponent.Alternatively, the tooth could be placed in close proximity, that is,separated by some amount such as 0.01 mm. In one possible embodiment,the user is allowed to modify the separation distance, such as byclicking on a suitable icon and selecting a new value for the separationdistance.

Other Embodiments and Features

[0064] A. Initial occlusal contact determination and occlusal contactdetermination during treatment

[0065] The occlusal contact determination can be made for the initial(maloccluded) condition of the patient's teeth. The patient's teeth arescanned (either directly or from a physical model) and then the scandata is converted into a 3D representation of the dentition. A biteregistration scan is performed, and the three-dimensional relationshipof the upper and lower arches of the teeth is obtained. The virtualmodels of the upper and lower arches can now be positioned in anoccluded condition and the process described above can be performed tofind the occlusal areas.

[0066] The identification and display of the occlusal contacts in theinitial condition is helpful in evaluating a proposed treatment planbecause it enables the practitioner to compare the initial and proposedtreatment plans in terms of occlusal contacts. For example, the userinterface could be organized into a split screen to show the occlusalcontacts for the lower jaw in the initial condition on the left handside and the occlusal contacts in the proposed treatment on the righthand side of the screen.

[0067] The determination of occlusal contacts can also be obtained anddisplayed at any time during treatment. During treatment, the upper andlower arches are scanned and a bite registration scan is taken.Preferably, for a bracket and wire type of treatment regime, the scansare performed in vivo using a hand-held 3D scanner such as described inthe published PCT patent application of OraMetrix, Inc. citedpreviously. Again, a qualitative assessment of the occlusal contacts canbe made to more completely assess the progress of treatment, and thecurrent stage of occlusal contacts can be compared to the expectedtreatment outcome and initial occlusal contacts to verify that thetreatment is progressing properly. In the event that the occlusalcontact detection and display results in a desire to change thetreatment, the treatment plan can be revised and the patient fitted witha modified orthodontic appliance. For example, the wire may be given amodified geometry to move the teeth into a more optimal position toincrease the occlusal contact area.

[0068] B. Dynamic detection of occlusal contacts

[0069] The present invention also provides for the ability to determineand display occlusal contacts dynamically, that is, the order andlocation at which the contacts occur when the patient's jaw are moveddynamically from an open to a closed condition. The 3D models of theupper and lower arches can be moved relative to one another to simulateclosing of the jaw or a chewing motion. This simulation can be done forinitial condition of the arches, or for the arches when the teeth aremoved relative to each other in a proposed treatment plan. The dynamicmodel of the motion of the mandible relative to the maxilla duringocclusion or chewing can be obtained via a variety of imagingtechniques, including video, X-ray, or successive scans of the upper andlower arches as the patient moves their teeth. The determination ofwhere the teeth are coming into contact during an occlusion or during achewing motion yields clinically important information that is helpfulin planning treatment, revising an initial treatment plan, or inconsideration of whether additional medical care is recommended for thepatient.

[0070] Thus, in another aspect, a method is provided for determining theproximity of teeth of upper and lower jaws of a patient comprising thesteps of:

[0071] a) storing data representing a three-dimensional model of teethfrom the upper and lower arches of the patient in a memory associatedwith a computer;

[0072] b) simulating motion of said upper and lower arches relative toeach other; and

[0073] c) calculating, with said computer and model, distances betweensurfaces of teeth in one of said upper and lower arches and surfaces ofteeth in the other of said upper and lower arches during said simulationof motion.

[0074] Information regarding the calculations can be illustrated to theuser on a display associated with the computer, such as showing theinitial contacts in one color, and all of the other occlusal contacts ina contrasting color or shading. The display of contact information canbe a static display of the teeth or in a dynamic simulation of themotion.

[0075] C. Tooth Wear and Occlusal Contact Monitoring

[0076] Many persons suffer from bruxism, a condition in which they grindtheir teeth, typically while they are asleep. Over time, the toothenamel is worn down, which can lead to other problems for the patientincluding decay or disease of the tooth. Detection and monitoring oftooth wear is an important diagnostic feature provided in one aspect ofthe present invention. The progress of the bruxism can be monitored bytaking a scan of the patient initially, taking a second scan at a laterpoint in time, and comparing the tooth models of selected teeth or allthe teeth before and after. For example, a subtraction feature isemployed by which the virtual model of a tooth at the later stage issubtracted from the model at the initial stage, with the differencebeing the portion of the tooth that has been worn away. A method ofmonitoring tooth wear is thus provided, comprising the steps ofobtaining a first three-dimensional virtual model of a portion of thepatient's dentition at a first point in time, obtaining a secondthree-dimensional virtual model of said portion of the patient'sdentition at a second, later point in time; and comparing said first andsecond virtual models to each other. The step of comparison can be asubtraction operation, which is typically provided in CAD/CAM software.The method continues with the step of identifying, from step ofcomparison, portions of the first three-dimensional virtual model thatare no longer present in said second three-dimensional model due to wearof the dentition. For example, the identifying step could be performedby illustrating on the display screen the first three-dimensional modelwith the areas worn away in a contrasting color or shading.

[0077] Alternatively, tooth wear can be monitored by measuring occlusalcontacts at two different points in time. By measuring the occlusalcontacts of the teeth both at an initial stage of treatment and at alater point in time, the occlusal contact areas can be compared to eachother. One would typically expect that the occlusal contact surface areawould increase in time, particularly in the areas where bruxism isoccurring. The evaluation of before and after occlusal contacts can bemade qualitatively, using a subjective visual assessment of the occlusalcontacts as displayed on a monitor, or it can be done quantitatively.For quantitative occlusal contact analysis, measurement tools such asfine grid can be placed over the region of the occlusal contacts and thesurface area of the occlusal contact measured or calculated either by ahuman operator or automatically using the computer.

[0078] The process can be extended to measurement of gingival recessionand erosion caused by tooth brushing or chemical erosion.

[0079] D. Contacts Between Teeth

[0080] The distance detection algorithms described herein can also beused to determine the interproximal contact points between teeth, eitherin an initial situation or in a proposed treatment plan for the patient.Optimal interproximal contact points between teeth is important to avoidimpaction of food between the teeth. The interproximal contact pointscan be identified by the algorithms explained previously for opposingteeth, except that the distance measurements are being made to theadjacent tooth. The technique of establishing parallel planes anddetermining where the planes intersect the teeth, as shown in FIGS. 8and 9, yields a set of lines, one line for each tooth. The distancebetween the lines is indicative of the interproximal distance. This is aparticularly useful approach. The interproximal contact points can thenbe displayed on the monitor of the workstation and evaluated by theuser.

[0081] The ability to quantitatively measure and display interproximalcontact points is a distinct advantage for an interactive treatmentplanning software program. In particular, it enables the user toposition each tooth relative to its neighbor in a manner such that theinterproximal contacts are optimized on a tooth by tooth basis. Thetreatment planning program preferably provides the orthodontist with theability to move each tooth relative to another tooth, for example rotateabout the tooth axis, tilt the tooth or move it up or down to optimizethe interproximal relationship with the adjacent teeth. The visualdisplay of interproximal contacts (such as in a green color where theseparation distance is less than a threshold such as 0.1 mm) gives theuser immediate feedback on the quality of the setup. Furthermore, as agiven virtual tooth is moved, the software is preferably programmed suchthat the occlusal contact display changes immediately to give instantvisual feedback as to the effect of tooth movement on occlusal contacts.

[0082] E. Restorative Dentistry and Dental Prosthetics

[0083] The occlusal contact and interproximal contact detection anddisplay can also be a highly useful feature in planning restorativedentistry. For example, if no orthodontic treatment is planned but thepatient is going to be given a crown, inlay, or other prosthetic device,the design and manufacture of the prosthetic device can be optimized interms of providing interproximal and occlusal contact. This is achievedby scanning the patient's dentition, including a bite registration scan,and designing the shape of the prosthetic device as a virtualthree-dimensional object on the computer. The design of the prostheticdevice takes into account the interproximal (and occlusal) relationshipto the other teeth. The three-dimensional shape of the prosthetic isoptimized on the computer so that when it is implanted in the patient itachieves a superior interproximal and occlusal relationship with therest of the patient's teeth.

[0084] In the specific case of crowns, crowns are typically made of goldusing a lost wax process in a dental lab. The lost wax process includesan intermediate step of creating a wax model of the crown. The wax modelcan be scanned using a 3D scanner and the crown represented as anindependent three-dimensional virtual object. The virtual object canthen be fitted to a virtual model of the tooth, in effect simulating theinstallation of the crown in the patient. This simulation can occur in aworkstation in the office of the dentist or in the lab. The dentist canevaluate the fit of the crown relative to the other teeth. If thedentist wishes to modify the shape of the crown, he or she canmanipulate the model to add or subtract or otherwise modify the shape ofthe crown. The 3D model can then be exported to a rapid prototypingmachine (such as, for example, stereolithography (SLA), laser 3Dprinting, etc.) for manufacture of a physical model of the crown. Theprocess proceeds with a manufacture of a crown in gold or porcelainhaving the modified configuration.

[0085] The process can also be extended to fillings, namely thedetection of occlusal contacts for filings and determination of highspots using the algorithms described herein. The challenge faced by thedentist is that as the filling is done the dentist asks the patient tobite down to detect the high spot. Invariably, the pressure from theocclusion fractures the partially set amalgam. Our approach is acontactless approach and eliminates that risk. Similarly for crowns, ourelectronic detection eliminates any interventional episodes forchairside correction of the crown to ensure better fit.

[0086] Similar concepts apply when designing other appliances andprosthetic devices, such as dentures. The process of design can becarried out on a computer using virtual tooth models and thedetermination, display and evaluation of interproximal and occlusalcontacts can be made on a workstation using the techniques describedherein so as to optimize the design of the appliance or device.

[0087] The method can be extended to designing and fabricating a set ofdentures for a patient and improving interproximal and occlusal contactof the teeth of the dentures. In this aspect, the method includes thesteps of obtaining a three-dimensional virtual model of teeth of upperand lower arches of the patient. This can be done for example usingtemplate teeth stored in memory (see the published PCT application ofOraMetrix, Inc., cited previously) or from a scan of the patient'steeth. The virtual model is stored in a computer, preferably a computerhaving treatment planning software. The teeth of the upper and lowerarches are moved relative to each other to a proposed arrangement for aset of dentures. Then, using the techniques described in detail herein,the computer calculates distances between surfaces of adjacent teeth andbetween surfaces of opposing teeth with the upper and lower arches in aclosed condition to assess the interproximal relationship and occlusalcontacts of the teeth. The computer displayes information associatedwith calculations on a user interface, such as by showing occlusalcontacts or interproximal contacts in a contrasting color or shading orusing a transition from white to color. The dentist then uses thetreatment planning software to adjust the position of one or more teethto more optimally position of the teeth relative to each other as aresult of the display of contact information. When the optimalarrangement is arrived at, the dentures are fabricated.

[0088] Not only can the above method be used for detecting denturecontacts, it can be applied to surgical splints that are implanted inthe patient's mouth. The design of the splint can be carried out on acomputer and a milling machine can grind them accurately even beforeinsertion.

[0089] F. Bracket, wire, and appliance location and conflicts

[0090] The above descriptions of occlusal and interproximal contactdetermination have assumed that one is measuring distance between teeth.The technique can be extended to determining distances between a toothand a portion of an orthodontic appliance, such as a bracket or wire.The technique can also be used for determining the distance betweenopposing brackets in the upper and lower arches or between a bracket andan opposing wire, or between opposing wires. For example, the distancebetween a tooth cusp and the bracket on the opposing tooth is calculatedusing one of the algorithms described previously. The virtual models ofthe upper arches will be typically placed in a closed or occludedcondition when this calculation is performed. The teeth and brackets arepresented as virtual objects on the workstation of the computer with theareas in which the distance between the bracket and tooth is less than athreshold highlighted in a contrasting color or shading or as a smoothtransition in color or shading. Actual collisions between the teeth andthe brackets can also be calculated and displayed. This feature againhelps the user evaluate a proposed treatment plan, including a proposedlocation of brackets on the teeth. The user is preferably able to modifythe location of the virtual brackets on the teeth and run a newsimulation of potential contact or collision between the appliance andthe teeth. The collision or conflict detection process can also beperformed based on actual location of the brackets on the patient'steeth, using a virtual model of the patient obtained from scanning ofthe patient.

[0091] Thus, in another aspect, a method is provided for determiningpotential conflicts in positioning of an orthodontic appliance on thedentition of the patient. The method comprises the steps of obtaining avirtual model of the upper and lower arches of patient's dentition;positioning a virtual model of an orthodontic appliance on at least oneof the arches of the virtual model of the dentition; placing the virtualmodels of the upper and lower arches in an occluded condition;calculating distances between portions of the virtual model of thedentition and portions of the virtual model of the orthodonticappliance, and displaying the virtual models of the upper and lowerarches and the orthodontic appliance on a user interface along withinformation associated with the calculations. The process can beextended to conflicts between brackets on opposing teeth, conflictsbetween brackets and gingival tissue, conflicts between brackets andwires in the opposing arch, and conflicts between upper and lowerarchwires.

[0092] Variations from the illustrated technique, methods and apparatusis contemplated without departure from the scope of the invention. Theterm “contrasting color or shading” in the claims, in reference to thedisplay of contact information, is intended to encompass the situationin which a transition of color occurs between portions of the toothwhich are not contacts and portions which are (i.e. distance to theopposing or adjacent tooth is less than a threshold), as well as thesituation in which no transition occurs and the portions below thethreshold are illustrated in a contrasting color or shading and theportions above the threshold are illustrated in the usual manner (e.g.,as white objects or in natural color). This true scope is to beascertained by reference to the appended claims.

We claim:
 1. A method for determining the proximity of teeth of upperand lower jaws of a patient, comprising the steps of: a) storing datarepresenting a three-dimensional model of teeth from the upper and lowerarches of the patient in a memory associated with a computer; and b)calculating, with said computer and model, distances between surfaces ofteeth in one of said upper and lower arches and surfaces of teeth in theother of said upper and lower arches when said arches are in an occludedcondition.
 2. The method of claim 1, further comprising the steps ofproviding a user interface for displaying said three-dimensional model,displaying at least one tooth of at least one of said arches on saiduser interface, and indicating on said display information associatedwith said calculations.
 3. The method of claim 2, wherein said step ofindicating comprises the step of displaying portions of said model in acontrasting color or shading relative to other portions of said model.4. The method of claim 2, wherein said step of calculating results in adetermination that the distances between portions of teeth in the upperand lower arches is less than zero, and wherein said portions areillustrated in a contrasting color or shading relative to other portionsof said model.
 5. The method of claim 1, wherein said three-dimensionalmodel of teeth comprises a proposed arrangement of teeth in the upperand lower arches for planning orthodontic treatment of said patient. 6.The method of claim 1, wherein said step of calculating distancesincludes the step of calculating distances in a uniform direction for aplurality of points on the surface of a tooth in said model.
 7. Themethod of claim 1, wherein said step of calculating includes the step ofdetermining a direction normal to the surface of a tooth in said modeland calculating said distance in said normal direction.
 8. The method ofclaim 1, wherein said step of calculating includes, for a plurality ofpoints on a surface of a tooth, the step of calculating a sphere aroundeach of said points, and enlarging the size of the sphere until thesphere intersects with a surface of a tooth on the opposing arch in saidmodel.
 9. The method of one of claims 1, 6, 7 or 8, wherein said step ofcalculating results in a determination that a portion of a tooth of oneof said arches intrudes into a portion of a tooth of the other of saidarches, and wherein the method further comprises the step of displayingon a user interface the said portions of said tooth in a manner suchthat a user can readily distinguish said portions.
 10. A method ofevaluating a proposed set-up of teeth in planning treatment for anorthodontic patient, comprising the steps of: obtaining athree-dimensional digital model of the teeth of the upper and lowerarches; moving said teeth to a proposed set-up for treating the patient;calculating distances between portions of said teeth in said upper andlower arches when said teeth are positioned in an occluded condition;and displaying said teeth to a user in a manner such that a user canreadily distinguish portions of said teeth in said upper and lowerarches in which the distance between said portions is less than apredetermined threshold.
 11. The method of claim 10, wherein saidpredetermined threshold is adjustable by the user.
 12. The method ofclaim 10, wherein said portions of said teeth are displayed in acontrasting color relative to other portions of said teeth in which saidcalculations of distances results in distances greater than saidthreshold.
 13. The method of claim 10, wherein said step of calculatingresults in a determination that a portion of a tooth of one of saidarches intrudes into a portion of a tooth of the other of said arches,and wherein the method further comprises the step of displaying on saiduser interface the said portions of said tooth in a manner such that auser can readily distinguish said portions.
 14. A machine for assistinga user in planning treatment for an orthodontic patient, comprising: acentral processing unit; a user interface; memory storing a set ofinstructions for said central processing unit and a data setrepresenting a set of virtual teeth of a patient including the teeth ofan upper arch and a lower arch; said instructions comprising treatmentplanning software enabling a user to move the virtual teeth to aproposed set-up; and wherein said instructions further comprise a set ofinstruction for determining at least one occlusal contact of said upperand lower arches of said virtual teeth in said proposed set-up when saidvirtual teeth are in an occluded condition; and wherein said set ofinstructions includes instructions for display of said virtual teeth onsaid user interface with said occluded contact displayed in a mannerreadily observable to said user.
 15. The machine of claim 14, whereinsaid set of instructions calculates distances in a uniform direction forpoints on the surface of teeth in one of said arches to teeth in theopposite arch.
 16. The machine of claim 14, wherein said set ofinstructions determines a direction normal to the surface of virtualteeth in one of said arches and calculates a distance in said normaldirection to a surface of teeth in the opposite arch.
 17. The machine ofclaim 14, wherein said set of instructions calculates a sphere aroundpoints on a surface of virtual teeth in one of said arch, and enlargesthe size of said sphere until intersection of said sphere with a surfaceof a tooth on the opposing arch occurs.
 18. The machine of one of claims15, 16, or 17, wherein the proposed set-up would result ininterpenetration of a tooth of one arch into a tooth of the opposingarch and said set of instructions displays on said user interface thelocation of said interpenetration in a manner such that a user canreadily observe said location.
 19. The machine of claim 14, wherein saidset of instructions further comprises an instruction permitting the userto adjust a distance variable indicative of an occlusal contact.
 20. Themachine of claim 14, wherein said set of instructions includes adistance parameter indicative of an occlusal contact.
 21. The method ofclaim 1, wherein said step of calculating distances comprises the stepof forming a set of parallel planes extending between said upper andlower arches, and determining where said planes intersect virtual teethof said upper and lower arches:
 22. The method of claim 10, wherein saidstep of calculating distances comprises the step of forming a set ofparallel planes extending between said upper and lower arches, anddetermining where said planes intersect virtual teeth of said upper andlower arches.
 23. A method of manipulating virtual teeth on a userinterface of a general purpose computer, said user interface including adisplay and a pointing device, said virtual teeth including a firstvirtual tooth and a second virtual tooth, said second virtual toothcomprising either an adjacent tooth or an opposing tooth of said firstvirtual tooth, comprising the steps of: selecting said first virtualtooth with said pointing device; moving said pointing device while saidfirst virtual tooth is selected so as to drag said first virtual toothin the direction of said second virtual tooth; and automatically movingsaid first virtual tooth so as to place said first virtual tooth intoproximity with said second virtual tooth without requiring said user todrag said first virtual tooth into proximity to said second virtualtooth, thereby simulating a magnetic attraction of said first virtualtooth to said second virtual tooth.
 24. The method of claim 23, whereinsaid close proximity comprises touching contact between said first andsecond virtual teeth.
 25. The method of claim 23, wherein said closeproximity comprises a predetermined separation distance.
 26. The methodof claim 25, wherein said predetermined separation distance is variableand defined by a user.
 27. The method of claim 1, wherein said datarepresenting a three-dimensional model of teeth comprises datarepresenting an initial malocclusion of said patient.
 28. The method ofclaim 1, wherein said data representing a three-dimensional model ofteeth comprises data representing a state of the patient's dentitionduring the course of treatment wherein said teeth have moved from aninitial malocclusion towards a final position and performing step b) forsaid model of teeth representing the dentition during the course oftreatment.
 29. The method of claim 28, further comprising the step ofdisplaying occlusal contact areas for said patient on a user interfaceas a result of said calculating step b).
 30. The method of claim 29,further comprising the step of performing steps a) and b) for datarepresenting a three-dimensional model of teeth comprising an initialmalocclusion, and displaying occlusal contact areas for said patient onsaid user interface as a result of said calculating step b) performed onsaid model of teeth comprising an initial malocclusion.
 31. The methodof claim 29, further comprising the step of modifying a treatment planfor said patient based on evaluation of said display of said occlusalcontact areas.
 32. A method for determining the proximity of teeth ofupper and lower jaws of a patient, comprising the steps of: c) storingdata representing a three-dimensional model of teeth from the upper andlower arches of the patient in a memory associated with a computer; d)simulating motion of said upper and lower arches relative to each other;and c) calculating, with said computer and model, distances betweensurfaces of teeth in one of said upper and lower arches and surfaces ofteeth in the other of said upper and lower arches during said simulationof motion.
 33. The method of claim 32, wherein said simulation of motioncomprises a simulation of a closing of said upper and lower arches. 34.The method of claim 32, wherein said simulation of motion comprises asimulation of a chewing motion of said upper and lower arches.
 35. Themethod of claim 32, further comprising the step of providing a userinterface for displaying said three-dimensional model, displaying atleast one tooth of said upper and lower arches on said user interface,and indicating on said display information associated with saidcalculations.
 36. The method of claim 35, wherein said step ofindicating comprises the step of displaying portions of said model in acontrasting color or shading relative to other portions of said model inwhich said distance between said portions is less than a predeterminedthreshold.
 37. The method of claim 35, wherein said step of calculatingresults in a determination that the distances between portions of teethin the upper and lower arches is less than or equal to zero, and whereinsaid portions are illustrated in a contrasting color or shading relativeto other portions of said model.
 38. The method of claim 32, whereinsaid three-dimensional model of teeth comprises a model of a proposedarrangement of teeth in the upper and lower arches for planningorthodontic treatment of said patient.
 39. The method of claim 32,wherein said three-dimensional model of teeth comprises a model of aninitial malocclusion of the patent.
 40. The method of claim 32, whereinsaid three-dimensional model of teeth comprises a model of anintermediate position of teeth during the course of treatment of saidpatient.
 41. The method of claim 32, wherein said step of calculatingdistances includes the step of calculating distances in a uniformdirection for a plurality of points on the surface of a tooth in saidmodel.
 42. The method of claim 32, wherein said step of calculatingincludes the step of determining a direction normal to the surface of atooth in said model and calculating said distance in said normaldirection.
 43. The method of claim 32, wherein said step of calculatingincludes the step of calculating a sphere around a plurality of pointson a surface of a tooth in said one arch of said model, and enlargingthe size of the sphere until the sphere intersects with a surface of atooth on the opposing arch in said model.
 44. A method of monitoringtooth wear, comprising the steps of: obtaining a first three-dimensionalvirtual model of a portion of the patient's dentition at a first pointin time; obtaining a second three-dimensional virtual model of saidportion of the patient's dentition at a second, later point in time;comparing said first and second virtual models to each other; andidentifying, from said step of comparison, portions of said firstthree-dimensional virtual model that are no longer present in saidsecond three-dimensional model due to wear of said dentition.
 45. Themethod of claim 44, wherein said step of comparing comprises the step ofsubtraction of said second three-dimensional model from said firstthree-dimensional model.
 46. A method of monitoring tooth wear,comprising the steps of: 1) obtaining a first three-dimensional virtualmodel of a portion of the patient's dentition at a first point in time,wherein said first virtual model comprises a virtual model of the upperand lower arches; 2) obtaining a second three-dimensional virtual modelof said portion of the patient's dentition at a second, later point intime; wherein said second virtual model comprises a virtual model of theupper and lower arches; 3) determining occlusal contact areas of saidupper and lower arches for said first three-dimensional model; 4)determining occlusal contact areas of said upper and lower arches forsaid second three-dimensional model; and whereby a comparison of saidocclusal contact areas from step 4) with said occlusal contact areas ofstep 3) provides an indication of tooth wear with an increase inocclusal contact area indicating tooth wear.
 47. The method of claim 46,wherein steps 3) and 4) comprise quantitative measurements of saidocclusal contact areas.
 48. The method of claim 47, wherein steps 1)-4)are performed in a general purpose computer and wherein saidquantitative measurements are performed automatically by said computer.49. A method for assessing the interproximal relationship of teeth in anarch of a patient, comprising the steps of: a) storing data representinga three-dimensional model of teeth from said arch in a memory associatedwith a computer; b) calculating, with said computer and model, distancesbetween surfaces of a first tooth in said arch to surfaces of a secondadjacent tooth in said arch; c) providing a user interface fordisplaying said arch; and d) indicating on said display informationassociated with said calculations.
 50. The method of claim 49, whereinsaid step of indicating comprises the step of displaying portions ofsaid first and second teeth in a contrasting color or shading relativeto other regions of said first and second teeth in which said distancebetween said portions is less than a predetermined threshold.
 51. Themethod of claim 49, wherein said step of calculating results in adetermination that the distances between portions of said first andsecond teeth is less than or equal to zero, and wherein said portionsare illustrated in a contrasting color or shading relative to otherportions of said teeth.
 52. The method of claim 49, wherein saidthree-dimensional model comprises a proposed arrangement of teeth forplanning orthodontic treatment of said patient.
 53. The method of claim52, further comprising the step of moving one of said first and secondteeth and repeating steps b) and d).
 54. The method of claim 49, whereinsaid step of calculating distances includes the step of calculatingdistances in a uniform direction for a plurality of points on thesurface of said first tooth.
 55. The method of claim 49, wherein saidstep of calculating includes the step of determining a direction normalto the surface of said first tooth and calculating said distance in saidnormal direction.
 56. The method of claim 49, wherein said step ofcalculating includes the step of calculating a sphere around a pluralityof points on a surface of said first in said one arch of said model, andenlarging the size of the sphere until the sphere intersects with asurface of said second tooth.
 57. The method of claim 49, said step ofcalculating distances comprises the step of forming a set of parallelplanes extending across said first and second teeth and evaluating thedistance between said first and second teeth long each of said planes.58. A method of improving interproximal and occlusal contact between atooth of a patient and a prosthetic device to be installed in thedentition of the patient in proximity to said tooth, comprising thesteps of: obtaining a three-dimensional virtual model of a portion ofthe dentition of the patient; storing the virtual model of the portionof the dentition in a computer; storing a virtual model of theprosthetic device in said computer; displaying said virtual model of theportion of the dentition and the virtual model of the prosthetic deviceon a user interface, with the virtual model of the prosthetic deviceplaced in a proposed position relative to the portion of the dentition;and adjusting the shape of the virtual model of the prosthetic device soas to optimize the occlusal and interproximal relationship of thevirtual model of the prosthetic device relative to the virtual model ofthe portion of the dentition; and fabricating the prosthetic device. 59.The method of claim 58, wherein the prosthetic device comprises a crown.60. The method of claim 58, wherein the prosthetic device comprises aninlay.
 61. The method of claim 58, wherein the prosthetic devicecomprises a bridge.
 62. The method of claim 58, further comprising thestep calculating, with said computer and said models, distances betweensurfaces of said prosthetic device and surfaces of an adjacent tooth insaid virtual model of a portion of the dentition.
 63. The method ofclaim 58, further comprising the step calculating, with said computerand said models, distance between surfaces of said prosthetic device andsurfaces of an opposing tooth in said virtual model of a portion of thedentition.
 64. The method of claim 62, further comprising the step ofdisplaying on said user interface portions of said virtual model of saidprosthetic device and portions of said adjacent tooth in which saiddistances are less than a predetermined threshold.
 65. The method ofclaim 62, further comprising the step of displaying on said userinterface portions of said virtual model of said prosthetic device andportions of said opposing tooth in which said distances are less than apredetermined threshold.
 66. A method of designing and fabricating a setof dentures for a patient and improving interproximal and occlusalcontact of the teeth of said dentures, comprising the steps of:obtaining a three-dimensional virtual model of teeth of upper and lowerarches of the patient; storing the virtual model in a computer; movingthe teeth of the upper and lower arches to form a proposed arrangementfor said set of dentures; calculating distances between surfaces ofadjacent teeth and between surfaces of opposing teeth with the upper andlower arches in a closed condition to assess the interproximalrelationship and occlusal contacts of said teeth; displaying informationassociated with said calculations on a user interface; adjusting theposition of one or more teeth to more optimally position of said teethrelative to each other as a result of said display; and fabricating thedentures.
 67. The method of claim 66, wherein the step of displayinginformation comprises the step of displaying portions of adjacent oropposing teeth in a contrasting color or shading for which the distancebetween said portions is less than a predetermined threshold.
 68. Amethod of determining potential conflicts in positioning of anorthodontic appliance on the dentition of the patient, comprising thesteps of: a) obtaining a virtual model of the upper and lower arches ofpatient's dentition; b) positioning a virtual model of an orthodonticappliance on at least one of the arches of the virtual model of thedentition; c) placing the virtual models of the upper and lower archesin an occluded condition; d) calculating distances between portions ofsaid virtual model of the dentition and portions of the virtual model ofthe orthodontic appliance. e) displaying the virtual models of the upperand lower arches and the orthodontic appliance on a user interface alongwith information associated with said calculations.
 69. The method ofclaim 68, wherein step e) further comprises the step of displayingportions of said virtual model of the dentition and portions of saidvirtual model of the orthodontic appliance in a contrasting color orshading for which the distance between said portions is less than apredetermined threshold
 70. The method of claim 68, wherein saidorthodontic appliance comprises a set of brackets.
 71. The method ofclaim 68, wherein said orthodontic appliance comprises an archwire. 72.The method of claim 68, wherein said portion of said dentition comprisesgingival tissue.